A MINLP model for optimal localization of pumps as turbines in water distribution systems considering power generation constraints

Pressure reducing valves (PRVs) are commonly used for pressure control in water distribution systems (WDSs) by means of dissipating the pressure excess. The use of pumps as turbines (PATs) is an alternative and more favorable system since they not only control the system pressure to decrease water leakage, but also utilize the pressure excess to generate electrical energy. The optimal localization of PATs can be casted into a mixed-integer nonlinear program (MINLP) where binary variables are used to represent the presence of PATs on links. Most of the available MINLP models for optimal PAT localization adopted the optimization approaches for PRV localization without considering the bound constraints on flow rates and heads of PATs. As a result, such an optimization model may make PATs delivering a non-desired output. In this paper, we propose a new MINLP model for optimal PAT localization. Instead of using a constraint on the maximum number of PATs to be placed in a WDS, new constraints relating to the minimum power generated by PAT are introduced to find links having adequate flows and head drops for placing PATs. Moreover, constraints are used to restrict flows and heads of PATs to their feasible operating range, so that the problem can be efficiently solved. The proposed MINLP model is applied to the optimal localization of PATs for a WDS benchmark and a real-world WDS in Vietnam. The results demonstrate that the new MINLP model can efficiently identify optimal locations for PAT placement where the specified working range and minimum power generated by the PATs are ensured.